Supplementary information supporting Nature 454, 88−91 (2008)

Vibrational excitation through tug-of-war inelastic collisions.
Stuart J. Greaves, Eckart Wrede, Noah T. Goldberg, Jianyang Zhang, Daniel J. Miller, and Richard N. Zare.
Nature 454, 88−91 (2008).   abstract   full text

See also the News & Views feature by Mark Brouard:
When molecules don't rebound.
Mark Brouard, Nature 454, 43−45 (2008).   full text

QCT movies of characteristic H + D₂(v = 0, j = 0) → H + D₂(v' = 3, j') inelastic collisions

We employ the quasi-classical trajectory (QCT) methodology as described in our two recent papers:
New, Unexpected and Dominant Mechanisms in the Hydrogen Exchange Reaction. JCP 128 164306 (2008).
A quasi-classical trajectory study of the time-delayed forward scattering in the hydrogen exchange reaction. JCP 128 164307 (2008).

5 million trajectories for H + D₂(v = 0, j = 0) collisions were propagated at a collision energy of E_col = 1.72 eV. Inelastically scattered trajectories for the D₂(v' = 3, j' = 0,2,4,6,8) product quantum states were analysed in more detail for comparison with experimental data by Zare and coworkers.

The D₂(v' = 3, j' = 0) product state

Figure 1 below [adapted from Figure 2 of Nature 454, 88−91 (2008)] shows the almost linear correlation of the impact parameter of the H atom before and the deflection angle of the H atom after the collision for the D₂(v' = 3, j' = 0) product state. Trajectories with low impact parameter are backwards scattered (the H atom turns around) whereas trajectories with high impact parameter are forward scattered (the H atom carries on in the same direction). Most trajectories are scattered on the nearside, i.e. into the same hemisphere as the incoming H atom.

Click on the links below or on the numbered areas of Figure 1 to start the corresponding trajectory movies.

	b / Å	Θ / deg
Traj 1	0.008	-170.9
Traj 2	0.067	156.1
Traj 3	0.130	164.3
Traj 4	0.282	134.4
Traj 5	0.302	131.8
Traj 6	0.424	107.3
Traj 7	0.603	73.5
Traj 8	0.716	55.9
Traj 9	0.804	42.1
Traj 10	0.813	40.2
Traj 11	0.999	1.8

Figure 1: Deflection angle, Θ, versus impact parameter, b, for D2(v' = 3, j' = 0) inelastically scattered products from QCT calculations of H + D2(v = 0, j =0) collisions at a collision energy of 1.72 eV.

The trajectory animations clearly show that the D-D bond is stretched due to the attractive forces between the incoming H atom and the nearest D atom in the molecule. The vibrational excitation of the D₂ results from the "tug" of the H atom as it departs and not, as is common wisdom for inelastic collisions, by compressing the D-D bond upon impact. Thus, the vibrational excitation is the result of a "tug of war" between the H atom and the D₂ molecule. These inelastic collisions are frustrated reactive scattering events in which the well between H and D never deepens enough to break the D-D bond to lead to HD products.

Remarks

• These trajectories are virtually planar, i.e., as shown in the movies. In order to lead to D₂(v' = 3, j' =0) products the D₂ molecule has to lie in the plane spanned by the H atom, its approach direction and the centre-of-mass of the D₂.

The D₂(v' = 3, j' = 4) product state

The same behaviour, i.e., that the product motion is set up by the final pull of the departing H atom, is seen in trajectories leading to higher rotational excitation. Figure 2 shows the scattering angle – impact parameter correlation for D₂(v' = 3, j' = 4) products which exhibits the same linear trend as for j' = 0, although less well defined.

	b / Å	Θ / deg
Traj 1	0.172	137.8
Traj 2	0.430	84.5
Traj 3	0.631	37.7
Traj 4	0.171	149.5
Traj 5	0.455	110.5
Traj 6	0.632	83.8
Traj 7	0.808	55.9
Traj 8	0.824	56.5
Traj 9	1.036	0.4
Traj 10	1.123	-15.9

Figure 2: Deflection angle, Θ, versus impact parameter, b, for D2(v' = 3, j' = 4) inelastically scattered products from QCT calculations of H + D2(v = 0, j =0) collisions at a collision energy of 1.72 eV.

Remarks

• The majority of trajectories leading to D₂(v' = 3, j' = 4) is not planar, i.e., the initial D₂ bond axis is oriented out of the plane of the H atom approach. The animated trajectories listed above were selected to be nearly planar so that the product rotation can clearly be seen in the movies. We have confirmed that non-planar trajectories show the same behaviour as the planar ones.
• Usually, the continuous quasi-classical quantum numbers (determined from the motions of the product molecule at the end of each trajectory) are rounded to the nearest integer (histrogram binning). One method to better reflect a product quantum state is to analyse only trajectories with restricted continuous quantum numbers, e.g., in the range 2.9 ≤ v'_QCT ≤ 3.1. Figure 2 shows only trajectories with vibrational quantum numbers restricted in this way so that the density of trajectories can still be discerned. Thus, the densities in Figures 1 & 2 are not comparable.

Eckart Wrede, 28 June 2008